In U.S. Pat. Nos. 4,070,611 and 4,165,479, and in British patent publication Nos. 2,079,946 and 2,079,463, there are described methods of producing images by a series of free induction signals, such that a Fourier transformation of the recorded data yields the image. Each signal is normally frequency-coded in one dimension by the application of a magnetic field gradient to the static magnetic field in which the sample is placed during signal recording. This gradient causes signal frequency to vary with position in the gradient direction. If a set of time-samples of one signal, S(m) for m=0 to M-1, is recorded, then a one-dimensional distribution P(k) of spins (or their properties) in the object is given by the discrete Fourier transform of the signal. ##EQU1## where c is some scaling factor.
Further, during the evolution of each free induction signal, second (or more) orthogonal gradients are switched on and off to give specific time-integrals of gradient. If, for example, a gradient G.sub.z has been applied over time T, then, in the recorded signal, phase depends on z as: .phi..sub.z =.gamma.z.intg.G.sub.z dt where .gamma. is the gyromagnetic ratio of the nuclei
This method of spatial coding is referred to herein as "phase encoding". The signal recording may occur more than once after each spin-excitation. In this case, time T is the total time for which G.sub.z has been applied since the last excitation.
After phase-encoding, decoding requires a set of signals with different imposed phase-twist. Continuing the above example, to produce an image of MxN independent pixels, it is necessary to take M samples from each of N signals. Each of the N signals is recorded after a different integral of G.sub.z, so that, for example, ##EQU2## where D is constant. The matrix P(k,l) giving spin-distribution in two dimensions in the sample is given by the two-dimensional discrete Fourier transform of the sampled signals S(m,n). ##EQU3## It may be seen that the set of N phase-encoded signals is decoded in the same way as the set of M frequency-coded samples. Whereas the evolution of the M samples occurs in real time, the N samples for a single value of m may be regarded as evolving in "pseudo-time". The method can be extended in more dimensions. (An LxMxN image, for instance, requires M samples from each of LxN signals.) The data in each phase-encoded dimension can be regarded as evolving in a "pseudo-time".
The data described is normally collected following several spin excitations rather than just one. It is normal to leave some spin-recovery period between excitation.
One of the problems associated with the Fourier transform methods described above is that most of the data-processing (the Fourier transformation) is left until all data has been collected despite time being available between sample exitations during the data-collection sequence. This can greatly increase the total time between starting data-collection and observing a completed image. The delay involved is due to the fact that Fourier transformation is carried out only when all the relevant data points have been acquired. In the 2-dimensional example of equation (4), for instance, each M-point transform (within square brackets) may be carried out as soon as the M samples of the relevant signals have been acquired, but the N-point transform cannot be started until more than N/2 signals have been recorded.